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Lecture 2:Resistive CircuitsNilsson 2.5, 3.1-3.4, 3.7

ENG17 : Circuits I

Spring 2015

April 2, 2015

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Overview

• Dependent Sources• Resistors in Series• Resistors in Parallel• Voltage Divider• Current Divider• Voltage / Current

Division• Δ-to-Y Equivalent

Circuits

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Finding vo

Strategy: • If we find io, we know vo• If we find iΔ, we know the dependent source• The current in 500V source is iΔ• Use KCL and KVL to do find unknown currents

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Finding vo

KVL: 500𝑉=5 𝑖Δ+20 𝑖0

KCL:

only 1 loop option

𝑖0=𝑖Δ+5 𝑖Δ=6 𝑖Δ

Ohm’s Law: 𝑣0=20 𝑖0

can only use node b or c

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Overview

• Dependent Sources• Resistors in Series• Resistors in Parallel• Voltage Divider• Current Divider• Voltage / Current

Division• Δ-to-Y Equivalent

Circuits

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Series Connected Elements

• Resistors in series carry the same current– KCL proves this

• Resistors in series can be summed– KVL proves this

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Overview

• Dependent Sources• Resistors in Series• Resistors in Parallel• Voltage Divider• Current Divider• Voltage / Current

Division• Δ-to-Y Equivalent

Circuits

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Parallel Connected Elements

• Resistors in parallel have same voltage across their terminals– KVL proves this

• Resistors in parallel can be summed inversely– KCL proves this– Conductances are summed

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Overview

• Dependent Sources• Resistors in Series• Resistors in Parallel• Voltage Divider• Current Divider• Voltage / Current

Division• Δ-to-Y Equivalent

Circuits

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Voltage Divider

• One voltage supply, multiple voltage levels

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Load

• RL = load = 1+ circuit elements that draw power from circuit– May alter voltage across parallel element

– But not if RL >> R2

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Example

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Example

• Wheatstone Bridge– 2 voltage dividers in parallel

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Overview

• Dependent Sources• Resistors in Series• Resistors in Parallel• Voltage Divider• Current Divider• Voltage / Current

Division• Δ-to-Y Equivalent

Circuits

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Current Divider

• One current supply, multiple current levels

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Example

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Example

• Similar analysis

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Overview

• Dependent Sources• Resistors in Series• Resistors in Parallel• Voltage Divider• Current Divider• Voltage / Current

Division• Δ-to-Y Equivalent

Circuits

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Voltage Division

• Generalization of voltage divider circuit

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Current Division

• Generalization of current divider circuit

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Example

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Overview

• Dependent Sources• Resistors in Series• Resistors in Parallel• Voltage Divider• Current Divider• Voltage / Current

Division• Δ-to-Y Equivalent

Circuits

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Unable to get Req

• For example, Wheatstone bridge circuit (below) cannot be simplified with standard parallel/series rules

• Must use circuit transformation

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Defining Delta/Pi and Y/T

Δ

Y T

π

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Delta-to-Wye Circuit Transformation

• Equivalent resistance between nodes• Note: resistor values are NOT THE SAME

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Apply to Wheatstone Bridge

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Recap

• Dependent Sources• Resistors in Series• Resistors in Parallel• Voltage Divider• Current Divider• Voltage / Current

Division• Δ-to-Y Equivalent

Circuits